Question

interpreting a graph
relationship between voltage & current
use the drop - down menus to select the correct answer
for each statement.
current is the dependent variable.
voltage is the independent variable.
this graph shows a(an) direct relationship.
a current of 0.04 a gives a voltage of v.
a voltage of 2 v corresponds to a current of a

Explanation:

Step1: Find the slope

The general form of a linear equation is \(y = mx + b\). In the context of voltage (\(V\)) and current (\(I\)), from Ohm's law \(V=IR\) (where \(R\) is the resistance, the slope of the line).
Take two points \((I_1,V_1)=(0.01, 2)\) and \((I_2,V_2)=(0.02,4)\). The slope \(R=\frac{V_2 - V_1}{I_2 - I_1}=\frac{4 - 2}{0.02-0.01}=\frac{2}{0.01}=200\space\Omega\)

Step2: Calculate voltage for \(I = 0.04\space A\)

Using \(V = IR\), substitute \(I = 0.04\space A\) and \(R=200\space\Omega\). Then \(V=(0.04)\times200 = 8\space V\)

Step3: Calculate current for \(V = 2\space V\)

Using \(I=\frac{V}{R}\), substitute \(V = 2\space V\) and \(R = 200\space\Omega\). Then \(I=\frac{2}{200}=0.01\space A\)

Answer:

A current of \(0.04\space A\) gives a voltage of \(8\space V\). A voltage of \(2\space V\) corresponds to a current of \(0.01\space A\)